Question

How do you prove `cos(x-pi/6) = 1/2([sqrt3] cosx + sin x)`?

Answer 1

See below

Explanation:

LHS =left hand side, RHS =right hand side

Use formula `cos(A-B)=cosA cosB + sinA sin B`

LHS `=cos x cos (pi/6) + sinx sin (pi/6)`

`=cos x xx sqrt 3/2 + sinx xx 1/2`

`=1/2 (sqrt 3 cosx + sinx)`

`= RHS`